A. ND Mathematics Content Standards, Grade 5 - ND Curriculum ...

such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tool s to explore and deepen their
understanding of concepts.
6. Attend to precision.
Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own
reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about
specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate acc urately and efficiently, express
numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated
explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.
7. Look for and make use of structure.
Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is
the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see
7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x 2 + 9x + 14, older students
can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an
auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some
algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y) 2 as 5 minus a positive number
times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.
8. Look for and express regularity in repeated reasoning.
Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students
might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By
paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students
might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x 2 + x + 1), and (x –
1)(x 3 + x 2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient
students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of t heir intermediate results.
North Dakota Mathematics Content Standards
Based on the Common Core State Standards
Introduction 7 June 2011